Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 111


$\ln 2$

Work Step by Step

Let $ u=\ln t $, then $ du =\frac{1}{t}dt $ and hence $ u $ changes from $\ln e=1$ to $\ln e^2=2$; thus we have: $$\int_{e}^{e^2} \frac{1}{t\ln t}dt=\int_{1}^{2} \frac{du }{u}=\ln u|_{1}^{2}\\ =\ln 2-\ln 1=\ln2. $$ where used the properties $\ln e=1$ and $\ln B^x=x\ln B $.
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